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Repeated Quiz Questions

Each week you get multiple attempts to take a two-question quiz. For each attempt, two questions are pulled at random from a bank of 100 questions. For a single attempt, the two questions are distinct.

  1. If you attempt the quiz 5 times, what is the probability that within those 5 attempts, you’ve seen at least one question two or more times?
  2. How many times do you need to attempt the quiz to have a greater than 50% chance of seeing at least one question two or more times?

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